242 citations · 546 across the 54 of their papers we have counts for
11 papers · 1 filter
Knot theory and cluster algebra III: Posets
Véronique Bazier-Matte, Ralf Schiffler
In previous work, we associated a module to every segment of a link diagram and showed that there is a poset isomorphism between the submodules of and the Kau…
Knot theory and cluster algebras II: The knot cluster
Véronique Bazier-Matte, Ralf Schiffler
To every knot (or link) diagram K, we associate a cluster algebra A that contains a cluster x with the property that every cluster variable in x specializes to the Alexander polyno…
Higher Dimer Covers on Snake Graphs
Gregg Musiker, Nicholas Ovenhouse, Ralf Schiffler +1
Snake graphs are a class of planar graphs that are important in the theory of cluster algebras. Indeed, the Laurent expansions of the cluster variables in cluster algebras from sur…
Perfect matching problems in cluster algebras and number theory
Ralf Schiffler
This paper is a slightly extended version of the talk I gave at the Open Problems in Algebraic Combinatorics conference at the University of Minnesota in May 2022. We introduce two…
Frieze Vectors and Unitary Friezes
Emily Gunawan, Ralf Schiffler
Let Q be a quiver without loops and 2-cycles, let A(Q) be the corresponding cluster algebra and let x be a cluster. We introduce a new class of integer vectors which we call frieze…
Continued fractions and orderings on the Markov numbers
Michelle Rabideau, Ralf Schiffler
Markov numbers are integers that appear in the solution triples of the Diophantine equation, , called the Markov equation. A classical topic in number theory, the…